Non-hyperbolic automatic groups and groups acting on CAT(0) cube complexes
2014 ◽
Vol 24
(06)
◽
pp. 795-813
We discuss a problem posed by Gersten: Is every automatic group which does not contain ℤ × ℤ subgroup, hyperbolic? To study this question, we define the notion of "n-track of length n", which is a structure like ℤ × ℤ, and prove its existence in the non-hyperbolic automatic groups with mild conditions. As an application, we show that if a group acts freely, cellularly, properly discontinuously and cocompactly on a CAT(0) cube complex and its quotient is "weakly special", then the above question is answered affirmatively.
2005 ◽
Vol 15
(05n06)
◽
pp. 875-885
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1998 ◽
Vol 08
(05)
◽
pp. 575-598
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Keyword(s):
2014 ◽
Vol 150
(3)
◽
pp. 453-506
◽
2017 ◽
Vol 60
(1)
◽
pp. 54-62
◽
Keyword(s):
2017 ◽
Vol 38
(6)
◽
pp. 2180-2223
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Keyword(s):
Keyword(s):